Thousands of times more pollution? Extraordinary claims require extraordinary evidence!
The energy content of wood varies based on how dry it is (obviously, water can't burn so you remove the water to increase the proportion of remaining mass that burns compared to the energy released when burning the combustible mass) abut ends up being approximately 15Mj/kg. Using an efficient wood stove you can extract about 70% of this energy as heat, for the purpose of heating and cooking.
The energy content of coal is about double that of wood. Typically we don't burn coal in home fires, rather we burn the coal in a large power plant, carry the energy as electricity then consume that energy in various forms at home. The typical efficiency of coal fired power plants is in the order of 30–40%. So you are basically at parity with wood fuel, with the convenience of a large power plant where it becomes economically viable to scrub ash and soot out of the exhaust.
So how much less pollution does as coal fired power plant produce than a wood fire at home? It turns out that scrubbers are anywhere from 95–99% efficient depending on design, energy input and maintenance.
So what we are left with is an estimate of the pollution produced by a wood fire being in the order of hundreds of times worse than pollution produced by the same energy production at a coal fired power plant. To qualify for "thousands" of times more pollution, the scrubbers at the coal fired plant would have to be 99.9% efficient without consuming a significant portion of the energy produced by the power plant (this is the goal of "clean coal" projects).